A Torsion Spring is a Spring That Works by Torsion or Twisting

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A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic objectthat stores mechanical energy when it is twisted. The amount of force (actually torque) it exerts

is proportional to the amount it is twisted. There are two types. A torsion bar is a straight bar of metal or rubber that is subjected to twisting (shear stress) about its axis by torque applied at its

ends. A more delicate form used in sensitive instruments, called a torsion fiber consists of a

fiber of silk, glass, or quartz under tension, that is twisted about its axis. The other type, a helicaltorsion spring, is a metal rod or wire in the shape of a helix (coil) that is subjected to twistingabout the axis of the coil by sideways forces ( bending moments) applied to its ends, twisting the

coil tighter. This terminology can be confusing because in a helical torsion spring the forcesacting on the wire are actually bending stresses, not torsional (shear ) stresses.

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Contents

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y 1 Torsion coefficient

y 2 Uses y 3 Torsion balance

y 4 Torsional harmonic oscillators o 4.1 Applications

y 5 See also y 6 References

y 7 Bibliography y 8 External links

[edit] Torsion coefficientAs long as they are not twisted beyond their elastic limit, torsion springs obey an angular form of

Hooke's law:

where is the torque exerted by the spring in newton-meters, and is the angle of twist from its

equilibrium position in radians. is a constant with units of newton-meters / radian, variouslycalled the spring's torsion coefficient, torsion elastic modulus, rate, or just spring constant,

equal to the torque required to twist the spring through an angle of 1 radian. It is analogous to the

spring constant of a linear spring.

The energy U , in joules, stored in a torsion spring is:



[edit] Uses

y Torsion bars are heavy torsion springs used to support automobile suspension components, allowing those components (which indirectly support the wheels) to move in

response to rough roads while allowing a smooth ride in the vehicle.

y The t orsion pendulum used in torsion pendulum clocks is a wheel-shaped weight

suspended from its center by a wire torsion spring. The weight rotates about the axis of the spring, twisting it, instead of swinging like an ordinary pendulum. The force of the

spring reverses the direction of rotation, so the wheel oscillates back and forth, driven atthe top by the clock's gears.

y The t orsion cat apul t or mangonel is a medieval siege engine invented by the ancient

Greeks. It uses a torsion spring consisting of twisted ropes to swing an arm that throws aheavy missile at the enemy with great force.

y The balance spring or hairspring in mechanical watches is a fine spiral-shaped torsionspring that pushes the balance wheel back toward its center position as it rotates back andforth. The balance wheel and spring function similarly to the torsion pendulum above in

keeping time for the watch.

y The D'Arsonval movement used in mechanical pointer-type meters to measure electrical

current is a type of torsion balance (see below). A coil of wire attached to the pointer twists in a magnetic field against the resistance of a torsion spring. Hooke's law ensures

that the angle of the pointer is proportional to the current.

y A DMD or digital micromirror device chip is at the heart of many video projectors. It

uses hundreds of thousands of tiny mirrors on tiny torsion springs fabricated on a siliconsurface to reflect light onto the screen, forming the image.

Other uses are in the large coiled torsion springs used to counter-balance the weight of garage

doors, and a similar system is used to assist in opening the trunk (boot) cover on some sedans.Small coiled torsion springs are often used to operate pop-up doors found on small consumer

goods like digital cameras and compact disc players. Strong coiled torsion springs are used in theconstruction of traditional springloaded-bar type mousetraps.

[edit] Torsion balance



Drawing of Coulomb's torsion balance. From Plate 13 of his 1785 memoir.

The torsion balance, also called torsion pendulum, is a scientific apparatus for measuring very

weak forces, usually credited to Charles-Augustin de Coulomb, who invented it in 1777, but

independently invented by John Michell sometime before 1783.[3]

Its most well-known uses were by Coulomb to measure the electrostatic force between charges to establish Coulomb's Law, and

by Henry Cavendish in 1798 in the Cavendish experiment[4]

to measure the gravitational force between two masses to calculate the density of the Earth, leading later to a value for the

gravitational constant.

The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as

a very weak torsion spring. If an unknown force is applied at right angles to the ends of the bar,the bar will rotate, twisting the fiber, until it reaches an equilibrium where the twisting force or

torque of the fiber balances the applied force. Then the magnitude of the force is proportional tothe angle of the bar. The sensitivity of the instrument comes from the weak spring constant of the

fiber, so a very weak force causes a large rotation of the bar.

In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ballattached to one end, suspended by a silk thread. The ball was charged with a known charge of

static electricity, and a second charged ball of the same polarity was brought near it. The twocharged balls repelled one another, twisting the fiber through a certain angle, which could be

read from a scale on the instrument. By knowing how much force it took to twist the fiber

through a given angle, Coulomb was able to calculate the force between the balls. Determiningthe force for different charges and different separations between the balls, he showed that itfollowed Coulomb's law.

To measure the unknown force, the spring constant of the torsion fiber must first be known. This

is difficult to measure directly because of the smallness of the force. Cavendish accomplishedthis by a method widely used since: measuring the resonant vibration period of the balance. If the

free balance is twisted and released, it will oscillate slowly clockwise and counterclockwise as a



harmonic oscillator , at a frequency that depends on the moment of inertia of the beam and theelasticity of the fiber. Since the inertia of the beam can be found from its mass, the spring

constant can be calculated.

Coulomb first developed the theory of torsion fibers and the torsion balance in his 1785 memoir, R

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t e des fils demet al &c. This led to its use in other scientific instruments, such as galvanometers, and the

Nichols radiometer which measured the radiation pressure of light. In the early 1900s

gravitational torsion balances were used in petroleum prospecting. Today torsion balances arestill used in physics experiments. In 1987, gravity researcher A.H. Cook wrote:

The most important advance in experiments on gravitation and other delicate measurements was the

introduction of the torsion balance by Michell and its use by Cavendish. It has been the basis of all the

most significant experiments on gravitation ever since.[5]

[edit] Torsional harmonic oscillators

For definition of terms see end of section

Torsion balances, torsion pendulums and balance wheels are examples of torsional harmonicoscillators that can oscillate with a rotational motion about the axis of the torsion spring,

clockwise and counterclockwise, in harmonic motion. Their behavior is analogous totranslational spring-mass oscillators (see Harmonic oscillator#Equivalent systems). The general

equation of motion is:

If the damping is small, , as is the case with torsion pendulums and balance wheels,

the frequency of vibration is very near the natural resonance frequency of the system:

The general solution in the case of no drive force ( ), called the transient solution, is:

where:

[edit] Applications



The balance wheel of a mechanical watch is a harmonic oscillator whose resonance frequency

sets the rate of the watch. The resonance frequency is regulated, first coarsely by adjusting

with weight screws set radially into the rim of the wheel, and then more finely by adjustingwith a regulating lever that changes the length of the balance spring.

In a torsion balance the drive torque is constant and equal to the unknown force to be measured, times the moment arm of the balance beam , so . When the oscillatory

motion of the balance dies out, the deflection will be proportional to the force:

To determine it is necessary to find the torsion spring constant . If the damping is low, this

can be obtained by measuring the natural resonance frequency of the balance, since the moment

of inertia of the balance can usually be calculated from its geometry, so:

In measuring instruments, such as the D'Arsonval ammeter movement, it is often desired that the

oscillatory motion die out quickly so the steady state result can be read off. This is accomplished

by adding damping to the system, often by attaching a vane that rotates in a fluid such as air or water (this is why magnetic compasses are filled with fluid). The value of damping that causes

the oscillatory motion to settle quickest is called the critical damping :

Definition of terms

Term Unit Definition

radians Angle of deflection from rest position

Moment of inertia

Rotational friction (damping)

Coefficient of torsion spring

Drive torque

Hz Undamped (or natural) resonance frequency

Undamped resonance frequency in radians

Hz Damped resonance frequency

Damped resonance frequency in radians

Reciprocal of damping time constant

rad Phase angle of oscillation

m Distance from axis to where force is applied



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A Torsion Spring is a Spring That Works by Torsion or Twisting

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